#lang racket
(require racket/trace)


(define (sqrt x)
  (sqrt-iter 1.0 x))
(define (sqrt-iter guess x)
  (new-if (good-enough? guess x)
      guess
      (sqrt-iter (improve guess x) x)))
(define (good-enough? guess x)
  (< (abs (- (square guess) x)) 0.001))
(define (improve guess x)
  (average guess (/ x guess)))
(define (abs x)
  (if (> x 0)
      x
      (- x)))
(define (average x y)
  (/ (+ x y) 2))
(define (square x)
  (* x x))

(define (new-if predicate then-clause else-clause)
  (cond (predicate then-clause)
        (else else-clause)))
(trace sqrt-iter)

(sqrt 9)
 